Master Thesis

P-release kinetic as a predictor for P-availability in the STYCS Trials

Marc Jerónimo Pérez y Ropero

Introduction

  • In my Internship I studied the current GRUD, particularly Mg, P and K

  • Fertilizer requirement models imply \(Y\sim STP + Clay\) & \(P-\text{Export}\sim STP + Clay\)

  • Currently only stationary measurement of STP are considered

  • Could a kinetic desorption-model better explain the soil status and yield data?

Experimental Setup

  • LTE STYCS, all treatment conditions equal except P-fertilization, which is in 6 Levels, 3 were considered(\(P0\),\(P100\),\(P166\))
  • 4 Sites regarded; Ellighausen, Rümlang-Altwi, Oensingen, Zürich-Reckenholz
  • 5 Sites, 4 blocks per site, 6 Treatment-Levels, 4 Repetitions
  • Years 2022 was modelled, kinetic data was collected for year 2022

Kinetic Model

The net-desorption was modeled using a first-order kinetic equation:

1. The Rate of Release: The change in P over time is proportional to the remaining desorbable P. \[\frac{dP}{dt}=k \times (P^S-P)\]

2. The Solution: When solved, this gives us the equation for the curve: \[P(t)=P^S \times (1-e^{-kt})\]

  • \(P^S\) (PS): The maximum desorbable P pool.
  • \(k\): The first-order rate constant.

Adapted Kinetic-Experiment Setup

QI: Replicability of kinetic model in STYCS

QI: Replicability (Step 1: The Data)

Our Goal: To find the best model for our kinetic data. First, here are the raw data points from the experiment.

QI: Replicability (Step 2: The Flawed Model)

We first tested the original, linearized method from the 1980s. As you can see from the dashed lines, the predictions provide a very poor fit to the actual data.

QI: Replicability (Step 3: The Successful Model)

Because the old method failed, we adopted a modern non-linear approach. The solid lines show our final model, which accurately captures the desorption process. This gave us high confidence in our derived \(k\) and \(PS\) parameters.

Could a kinetic desorption-model better explain the soil status and yield data?

Relevant Variables

Soil Variables:

  • \(P-CO_2\) & \(P-AAE10\) stand for the GRUD STP-measurements in [\(g~P/kg ~ Soil\)]
  • \(k\)(\(s^{-1}\)) can be interpreted as the relative speed of net-desorption of orthophosphate
  • \(k*PS\)(\(g~Ps^{-1}\)) can be interpreted as the average net-release speed
  • \(PS\)(\(mg~P/L~H_2O\)) is the equilibrium concentration of \(PO_4^{3-}\) of the net-desorption experiment
  • From the 0-20cm Horizon: Clay-, Silt-,\(C_{org}\)-content and pH

Yield Variables:

  • For a year \(X\) and crop \(C\) \(Y_{main-rel}\) stands for \(Y_{main-rel}:=Y_C^{X}/mean(Y_C~\text{in year}~X~\text{in CH})\)
  • For every year:site:crop combination the yield was normalised using: \(Y_\text{norm}:=Y/median(Y_{P166})\)
  • The P-Export was calculated as the P-Uptake of the main product
  • The P-Balance was calculated as the difference \(P_{Fertilized}-\text{P-Export}\)

Research Questions

  • I: Is the method presented by Flossmann and Richter (1982) with the double extraction replicable with the soils from the STYCS-trial?
  • II: How do GRUD-measurements of STP correlate to the soil properties \(C_\text{org}\)-content, clay-content, silt-content and pH?
  • III: Are the kinetic coefficients \(k\) and \(PS\) correlated to soil properties?
  • IV: How well can current GRUD methods of STP (\(P-CO_2\) & \(P-AAE10\)) predict the Yield-parameters, P-Export and P-Balance?
  • V: How well can the kinetic parameters \(k\) & \(PS\) predict Yield-parameters, P-Export and P-Balance?

QI: Replicability of kinetic model in STYCS

QII & III: STP, k & PS correlate to soil properties?

The following random structure was chosen:

(1|year) + (1|Site) + (1|Site:block) + (Treatment|Site)

Do P-CO2, P_AAE10, k and PS correlate with soil characteristics?

Coefficient Table for Soil Covariates. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor PS k log(k*PS) CO2 AAE10
(Intercept) -1.772 -0.425 0.039 -0.536 -0.532
Alox -0.660 -1.204 -0.034 -0.319
Feox 0.020 -0.571 -0.164 -0.138
soil_0_20_clay 1.798 -1.733** 0.611 -0.007 -0.121
soil_0_20_Corg 1.044** -0.412 0.166 0.232
soil_0_20_pH_H2O 0.000 -0.280 0.094 0.075 0.057
soil_0_20_silt 0.252 0.113 -0.084 0.012
R2m 1.000 0.204 0.224 0.125 0.280
R2c 1.000 0.963 0.976 0.724 0.832

Observation

  • P-CO2 and P-AAE10 did not correlate with clay-content
  • k does not correlate with Treatment but with pH and silt-content
  • \(k*log(PS)\) had significant effects for clay- and silt-content as well as pH, but lower in Treatment
  • PS was the covariate best predicted by soil properties: \(R^2_m=0.858\)

QIV & V: Correlation k, PS & STP to Yield and P-metrics

Yield model summary:

Coefficient Table for Yield Variables. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor Yn-STP-CO2 Yn-STP-AAE10 Yn-STP-GRUD Yn-Kinetic Yr-STP-CO2 Yr-STP-AAE10 Yr-STP-GRUD Yr-Kinetic
(Intercept) 0.012 0.007 -0.109 0.156 -0.323 -0.257 -0.306 -0.119
k 0.166 -0.018
k:log(PS) -0.012 0.016
log(PS) 0.066 0.010
log(soil_0_20_P_AAE10) 0.067* 0.432** 0.037 0.046
log(soil_0_20_P_CO2) 0.027 -0.128 -0.001 -0.040
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) 0.149* -0.021
R2m 0.012 0.084 0.291 0.019 0.000 0.011 0.020 0.002
R2c 0.083 0.361 0.436 0.045 0.618 0.698 0.696 0.807

Observation

  • \(k*log(PS)\) and \(k\) showed the strongest effects in the prediction of Ynorm and Yrel
  • P-AAE10 did show a significant effect in prediction of Yrel

P-Export model summary:

Coefficient Table for P-export. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor CO2_Pexport AAE10_Pexport Grud_Pexport Kin_Pexport
(Intercept) 0.012 -0.002 0.119 0.596
k -0.014
k:log(PS) 0.080
log(PS) -0.018
log(soil_0_20_P_AAE10) 0.025 -0.015
log(soil_0_20_P_CO2) 0.087 0.131
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) 0.011
R2m 0.012 0.001 0.016 0.004
R2c 0.654 0.685 0.796 0.789

Observations

  • P-CO2 did show strong effects in predicting Pexport

P-balance model summary:

Coefficient Table for P-balance. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor CO2_Pbalance AAE10_Pbalance Grud_Pbalance Kin_Pbalance
(Intercept) 0.569* 0.315 0.610* 1.086*
k 0.155
k:log(PS) -0.151
log(PS) 0.341***
log(soil_0_20_P_AAE10) 0.009 0.009
log(soil_0_20_P_CO2) -0.023 -0.029
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) 0.030
R2m 0.001 0.000 0.006 0.122
R2c 0.590 0.762 0.596 0.699

Observation

  • \(PS\) showed the strongest effect in predicting P_balance and k showed substantial \(R^2_m\)

Concluding Remarcs

  • The net-desorption of P probably follows a first-order-kinetic, but \(PS\) is difficult to directly estimate.
  • The kinetic parameters \(k\) and \(PS\) could comparably and sometimes better explain Ynorm, Yrel and P-Balance.
  • Regarding the difference between \(R^2_m\) and \(R^2_C\) confounded effects seem to be buried in the sites.
  • P-CO2 and P-AAE10 are not as well explainable as \(PS\) and \(k\), in particular not by clay-content.
  • P-CO2 correlated however significantly with P-Export

Thank you for your attention